calculating reasonable royalty damages using conjoint analysis · conjoint analysis called consumer...

AIPLA QUARTERLY JOURNAL

Volume 45, Number 2 Page 233 Spring 2017

CALCULATING REASONABLE ROYALTY DAMAGES

USING CONJOINT ANALYSIS

Greg Allenby, Peter E. Rossi, Lisa Cameron, Jeremy Verlinda, and Yikang Li *

I. INTRODUCTION ................................................................................................ 234 II. BACKGROUND: THE ECONOMIC FRAMEWORK FOR CALCULATING

REASONABLE ROYALTIES ................................................................................. 235 III. THE ROLE OF CONJOINT ANALYSIS ................................................................. 238 IV. USING CONJOINT ANALYSIS TO ASSESS PATENT DAMAGES .......................... 241

A. Using the MSM to Assess the Defendant’s MPP .............................. 243 B. Using the EPM to Assess the Defendant’s MPP ............................... 249

V. CONCLUSIONS: COMPARISON OF APPROACHES USING CONJOINT

ANALYSIS TO ASSESS DAMAGES ...................................................................... 252

LIST OF TABLES

1. Table 1. Sample Choice Task ................................................................... 239

2. Table 2. Hypothetical Respondent’s Valuations of Two Camera

Profiles: Market Share Method (MSM) .................................... 246

3. Table 3. Hypothetical Respondent’s Valuations of Two Camera

Profiles: Equilibrium Profit Method (EPM) ............................ 249

* © 2017 Greg Allenby, Peter E. Rossi, Lisa Cameron, Jeremy Verlinda, and

Yikang Li. Greg Allenby is the Helen C. Kurtz Chair in Marketing, and a

Professor of Statistics at The Ohio State University’s Fisher College of

Business. Peter E. Rossi is the James Collins Professor of Marketing,

Statistics, and Economics at UCLA’s Anderson School of Management. Lisa

Cameron is a Principal at The Brattle Group, an economic consulting firm

that supports and provides expert testimony in litigation matters. Jeremy

Verlinda is a Senior Associate at The Brattle Group. Yikang Li is a Senior

Analyst at The Brattle Group. Professors Allenby and Rossi are both senior

academic advisors to The Brattle Group.

234 AIPLA Q.J. Vol. 45:2

I. INTRODUCTION

In many recent high-stakes patent disputes, plaintiffs’ experts have

measured reasonable royalty damages using data obtained from conjoint

surveys.1 While the use of conjoint analysis in patent disputes is becoming

increasingly popular, the method involves a number of highly technical analyses

and calculations.2

This article provides a user-friendly primer on methods that use conjoint

analysis to determine reasonable royalty damages. We present detailed

descriptions of two such methods referred to here as the Market Share Method

(“MSM”) and the Equilibrium Profit Method (“EPM”). Both the MSM and the

EPM focus on measuring profit that the alleged infringer would earn by,

hypothetically, selling a non-infringing version of its product.3 The MSM makes

1 See, e.g., Visteon Glob. Tech., Inc. v. Garmin Int’l, Inc., No. 10-CV-10578, 2016

WL 5956325, at *2–6 (E.D. Mich. Oct. 14, 2016); Apple, Inc. v. Samsung Elecs.

Co., 67 F. Supp. 3d 1100, 1120–21 (N.D. Cal. 2014); TV Interactive Data Corp.

v. Sony Corp., 929 F. Supp. 2d 1006, 1020–22 (N.D. Cal. 2013); Apple, Inc. v.

Motorola, Inc., 869 F. Supp. 2d 901, 905 (N.D. Ill. 2012); Apple, Inc. v.

Samsung Elecs. Co., No. 11-CV-01846-LHK, 2012 WL 3283478, at *7 (N.D.

Cal. Aug. 9, 2012); Memorandum Opinion and Order at 4–5, Memorandum

Opinion, VirnetIRNETX IncNC. v. Cisco Systems, Inc., No. 6: 10-CV-417

(E.D. Tex. Mar. 23, 2017) (No. 754); Memorandum Opinion and Order at 3–4,

ContentGuard Holdings, Inc. v. Amazon.com, Inc., No. 2:13-CV-1112-JRG

(E.D. Tex. Aug. 26, 2016) (No. 825); Order at 18, Microsoft Corp. v. Motorola,

Inc., No: C 10-1823JLR (W.D. Wash. May 4, 2016) (No. 490); Memorandum

Opinion at 9–10, Rembrandt Social Media, LP v. Facebook, Inc., No. 1:13-CV-

158 (E.D. Va. Apr. 4, 2016) (No. 351); Order re Apple’s Motion to Exclude the

Surveys, Expert Reports, and Opinions of Howard Marylander and James

Berger and References thereto by Joseph Gemini at 4–5, NetAirus Tech., LLC

v. Apple, Inc., No. LA 10-CV-03257 (C.D. Cal. Jan. 20, 2015).

2 See infra Part III (explaining in more detail that a conjoint survey is an

advanced market research technique involving asking survey respondents to

choose among various product profiles). Certain statistical methods—

referred to collectively as conjoint analysis—are applied to these survey data

to determine which product attributes were the drivers of the respondents’

choices among the given profiles. See Lisa Cameron et al., The Role of Conjoint

Surveys in Reasonable Royalty Cases, LAW360 (Oct. 16, 2013, 6:37 PM),

http://www.law360.com/articles/475390/the-role-of-conjoint-surveys-in-

reasonable-royalty-cases [https://perma.cc/4AET-TL85].

3 Typically, in these cases, the defendant has never sold a non-infringing

version of its product, which makes a calculation of profit based on real

2017 Calculating Reasonable Royalty Damages 235

the simplifying assumption that the alleged infringer charges the same price for

infringing and non-infringing versions of its product.4 In contrast, the EPM

allows the alleged infringer to adjust its price in response to the actions of its

competitors and changes in production costs.5 The latter method is more

theoretically sound but involves more complex calculations and assumptions

about the behavior and costs of competing firms. 6

The article proceeds as follows. First, it reviews the economic framework

that lies behind the calculation of reasonable royalty damages. Second, it

provides additional background on the conjoint survey itself, explaining how

such a survey elicits consumers’ valuations of an infringing feature in a complex,

multi-featured product. Third, it explains how the MSM and EPM are

implemented and concludes with a brief review of the relative merits of these

and other methods that rely on conjoint analysis to determine reasonable royalty

damages.

II. BACKGROUND: THE ECONOMIC FRAMEWORK FOR CALCULATING

REASONABLE ROYALTIES

In a reasonable royalty case, the goal of the damages calculation is to

determine the amount of money that the alleged infringer (“defendant”) would

need to pay the patent holder (“plaintiff”) to put the plaintiff in the same

economic position that it would have been in if the infringement had not

occurred.7 This goal is often formulated in terms of estimating the royalty

amount that would have been agreed to in a hypothetical negotiation between

the plaintiff and the defendant at the time of first infringement.8 The hypothetical

negotiation is an economically reasonable approach for calculating damages

because, in many cases, the loss suffered by the plaintiff as a result of the

defendant’s infringement is indeed the failure to collect license royalties that it

world data impossible. Hence, the damages expert uses conjoint analysis to

determine how much profit the defendant would have made on the sales of

this non-infringing version of its product in the market.

4 See infra Section IV.A.

5 See infra Section IV.B.

6 See, e.g., Greg M. Allenby et al., Valuation of Patented Product Features, 57 J.L.

ECON. 629, 630 (2014).

7 See, e.g., MARK A. GLICK ET AL., INTELLECTUAL PROPERTY DAMAGES: GUIDELINES

AND ANALYSIS 151–52 (2002).

8 Id.


would reasonably have collected “but for” the infringement of the plaintiff’s

patent.9 The basic economic principle governing the negotiation is that a rational

actor will only enter into agreements that make it better off.10 This consideration

determines “the boundaries of a mutually beneficial license,” when one exists.11

In such a negotiation, the patent-holding plaintiff will accept nothing less than

the opportunity cost associated with granting the license to the defendant, while

the defendant will be willing to pay nothing more than its potential profit

attributable to use of the license.12

The Georgia Pacific factors provide a standard framework for determining

the reasonable royalty that would emerge from the hypothetical negotiation.13

These factors address three general considerations that impact the reasonable

royalty for the license at issue: (i) information provided by existing licenses

regarding the likely royalty amount; (ii) costs to the licensor of granting a license;

and (iii) benefits to the licensee of obtaining a license.14

Clearly, when the same intellectual property has already been licensed

out to firms that are in a similar position to the defendant, the information

provided by these firms’ license payments can be invaluable in establishing the

reasonable royalty in the case at issue.15 In the absence of such data, however, the

damages expert will want to determine: (i) the minimum amount that the

plaintiff would be willing to accept for the license and (ii) the maximum amount

that a defendant would be willing to pay for the license (which we will refer to,

9 Id. at 152.

10 Cf. id. at 156 (explaining that “a rational economic agent will not willingly

enter into an agreement that makes him worse off”).

11 See id. at 156–57 (explaining how the Georgia-Pacific factors consider both the

hypothetical licensor’s costs and benefits in granting a license).

12 Id. at 157.

13 Georgia-Pacific Corp. v. U.S. Plywood Corp., 318 F. Supp. 1116, 1120

(S.D.N.Y. 1970) (providing fifteen factual considerations relevant to

determining the amount of a reasonable royalty).

14 GLICK ET AL., supra note 7, at 153 (explaining that Georgia-Pacific factors 1, 2,

and 4 consider whether other licenses provide useful information; factors 4

and 5 consider costs to the licensor of granting a license; and 6, 8, 9, 10, 11,

12, and 13 consider the benefits to the licensee of obtaining a license).

15 Id. (“The Georgia-Pacific factors 1, 2, and 4 direct us to examine whether other

licenses provide useful information.”).


hereinafter, as the defendant’s “maximum potential payment,” or “MPP”).16 The

value of the license will typically lie somewhere in the range defined by these

two figures.17

Given that the defendant’s MPP provides the upper bound on the

damage figure, a plaintiff will usually focus the damages analysis on calculating

the defendant’s MPP. When the patent is tied to a particular product feature, the

defendant’s MPP is equal to the difference between: (i) the profit that the

defendant earns from selling the product with the allegedly infringing feature

and (ii) the profit that the defendant would earn from selling the exact same

product (in terms of brand and other relevant characteristics) without this

feature. 18 In some cases, market data will be available to facilitate the calculation

of the defendant’s profit on each version of its product. For example, we may be

able to observe the defendant’s sales of its product before and after the addition

of the infringing feature, or the defendant may have sold its product with the

infringing feature in some geographic areas and without the infringing feature in

others.

In many cases, however, we do not observe such “natural

experiments.”19 As a result, plaintiffs are increasingly turning to conjoint

16 Georgia-Pacific Corp., 318 F. Supp. at 1121 (“[The] approach . . . requires

consideration not only of the amount that a willing licensee would have

paid for the patent license but also of the amount that a willing licensor

would have accepted.”) (alteration added). This amount is also often

referred to as the defendant’s maximum willingness to pay. However, we

use the term MPP to avoid confusion with a term of art frequently used in

conjoint analysis called consumer willingness to pay.

17 There are exceptions to this rule of thumb. For example, if the plaintiff

competes in the same market as the defendant and is seeking reasonable

royalty damages—as opposed to lost profits—the appropriate damages

figure could potentially exceed the defendant’s MPP.

18 See Allenby et al., supra note 6, at 631–33. Note that in some cases, the

defendant will need to drop the feature entirely in order to avoid

infringement. In other cases, the defendant can modify the feature at issue so

that it is no longer infringing. Often, the defendant will require some time to

modify its product so that it is no longer infringing the patent at issue.

However, in our analysis, we assume for the sake of simplicity that the

infringing feature can be modified or removed instantaneously.

19 Cameron et al., supra note 2.


analysis,20 which can be used to determine respondents’ valuations of infringing

and non-infringing versions of the product even when both products are not

available on the market at the same time.21

The next section outlines a hypothetical situation in which the plaintiff’s

expert runs a conjoint survey to determine how much consumers value the

defendant’s product without the infringing feature. It reviews the key elements

of a conjoint survey and discusses several approaches towards estimating the

defendant’s MPP using conjoint survey data.

III. THE ROLE OF CONJOINT ANALYSIS

Consider a case in which a plaintiff has patented the means for including

a Wi-Fi connection in a camera. Suppose further that there is a single producer

whose camera allegedly infringes the patent, while the other producers offer

cameras with no Wi-Fi connection at all.22

In the absence of suitable data on the defendant’s sales of its camera with

and without the infringing feature, the plaintiff’s damages expert may analyze

consumer preferences for an infringing and non-infringing version of the

defendant’s camera using data obtained from a conjoint survey. In such surveys,

respondents must make a series of choices among product profiles with different

sets of features.23

20 Id.

21 See Allenby et al., supra note 6, at 632–33. The inability to observe products

with and without the infringing feature in the marketplace at the same time

is a fundamental problem in patent damages analysis. This same problem

arises in product mislabeling cases. Typically, in such cases, we observe the

market price of a product with a claim that is alleged to be fraudulent, but

we do not observe the market price of the same product without the accused

claim. In these product mislabeling cases, the role of conjoint analysis is to

determine to what extent the claim influences or enhances demand for the

product.

22 For the sake of simplicity, the discussion throughout this paper assumes that

no other seller has access to the infringing feature.

23 See Cameron et al., supra note 2. Survey respondents are screened for

inclusion in the survey if they are willing and able to purchase the product.

This is because the survey is meant to represent that portion of the

population (say, U.S. residents) that may be willing to pay for the good or

service. Respondents are anticipated to be active in the purchase decision (or


For example, a conjoint survey designed to assess the defendant’s MPP

with respect to an infringing Wi-Fi feature may ask a respondent to make a series

of choices among camera profiles comprised of the following four features:

brand, availability of Wi-Fi connection, resolution, and price.24 These features are

often referred to as attributes, while the values that characterize each attribute

are referred to as levels.25

Table 1. Sample Choice Task

Table 1 provides a single choice task for this study. In this choice task, for

example, the brand attribute takes on three levels: X, Y, and Z.26

Profile 1 Profile 2 Profile 3 Profile 4

Brand X Y Z

Wi-Fi Yes No No

Resolution High Low High

Price $60 $60 $50

Purchase

none of

these

In the case of complex, multi-featured products, the conjoint survey will

focus on only a subset of product attributes.27 Nonetheless, the choice of

attributes included in the survey should not have a significant impact on the

results because respondents are told to hold constant attributes—such as the

zooming capability of the lens or the camera screen size—that are not included in

the survey.28

recently active) and are assumed to have some knowledge of the brands and

prices available in the marketplace.

24 Id.

25 Id.

26 Similarly, the Wi-Fi attribute has two levels: yes and no. The resolution

attribute has three levels: high, medium, and low. Finally, the price attribute

can take on four levels: $40, $50, $60, and $70. Note that not all of these

alternatives are depicted in the single choice task depicted in Table 1.

27 The need to focus on a subset of attributes arises because extensive

experience with conjoint surveys has shown that consumers cannot

effectively weigh more than seven attributes. See, e.g., Paul E. Green & V.

Srinivasan, Conjoint Analysis in Marketing: New Developments with Implications

for Research and Practice, 54 J. MARKETING, Oct. 1990, at 8–9.

28 See e.g., Cameron et al., supra note 2. As noted in this article, under some

circumstances the concern may arise that consumers hold different views on


Profile 4 in Table 1 is often referred to as the “no choice” option.29

Respondents select this profile when none of the other profiles is attractive

enough to trigger a purchase. The “no choice” option indicates that the consumer

chooses either to buy other brands of cameras with attributes and prices that are

not explicitly described, or to make no purchase because the prices and attributes

of the brands in the choice task are unattractive.30 The inclusion of the “no

choice” option in the choice task prevents the conjoint survey from forcing the

respondent to choose among the limited number of profiles described in the

choice task.

Conjoint surveys provide much more accurate information on consumer

preferences than an approach in which survey respondents are asked directly

how much they value individual product features (such as a Wi-Fi connection

embedded in a camera).31 This is because respondents in a conjoint survey are

asked to choose among product profiles just as they might do in a real shopping

situation.32 In contrast, experience with direct questioning in market research

shows that it is particularly difficult to obtain reliable stated values for products

that consumers do not buy regularly or that require unfamiliar trade-offs.33

“Today, most conjoint surveys are conducted in an online setting where

survey respondents must choose among product profiles with different basic

which attributes are being held constant. Differing consumer perceptions of

what is being held constant, however, will be a lesser concern when survey

respondents are familiar with the product under consideration. It is also

important to recognize that some brands may have unique features (i.e., the

operating system of an Apple iPhone 6) that need not be mentioned in the

conjoint survey but will instead be captured as part of the brand attribute.

29 See id.; See also Allenby et al., supra note 6, at 640. The “no choice” option is

also sometimes referred to as the “no buy” option.

30 See Allenby et al., supra note 6, at 644.

31 See Olivier Toubia et al., Optimization-Based and Machine-Learning Methods for

Conjoint Analysis: Estimation and Question Design, in CONJOINT MEASUREMENT:

METHODS AND APPLICATIONS 231, 233 (Anders Gustafsson et al. eds., 4th ed.

2007); see also, BRYAN K. ORME, GETTING STARTED WITH CONJOINT ANALYSIS:

STRATEGIES FOR PRODUCT DESIGN AND PRICING RESEARCH 18 (2006); Greg M.

Allenby et al., Incorporating Prior Knowledge into the Analysis of Conjoint

Studies, 32 J. MARKETING RES. 152, 152–53 (1995).

32 See Cameron et al., supra note 2.

33 Id.


features.”34 Respondents to conjoint “surveys typically perform between 12 and

20 ‘choice tasks’” like the one illustrated in Table 1.35 Each respondent-task

provides a data point for the analysis. Hence, if 400 respondents take the survey

and each respondent makes twenty choices, there will be 8,000 data points in the

analysis. The attribute levels associated with the profiles change across the choice

tasks and respondents vary their choices in response to these changes.36

Given these types of data, the damages expert can then perform a

statistical analysis—referred to as conjoint analysis—in which he uses each

respondent’s choices to determine how much each level of each attribute

contributes to the respondent’s overall valuation of the product.37 “This

contribution is referred to as the ‘part-worth’ of the attribute level.”38 “In the

patent infringement context, the part-worths are a key input in the determination

of [the defendant’s MPP, and hence] the reasonable royalty.”39 It should be noted

that part-worths are measured in utils; in economic parlance, the term util is a

measure of utility or value.

IV. USING CONJOINT ANALYSIS TO ASSESS PATENT DAMAGES

This section explains how the part-worths obtained through conjoint

analysis are used to assess reasonable royalty damages. As noted above, the

upper bound on reasonable royalty damages will typically be the defendant’s

MPP, which is the difference between the defendant’s profit in two worlds: (i)

the “infringing world” in which the defendant sells a product that includes the

infringing feature and (ii) the “non-infringing world” in which the defendant

34 Id. Survey respondents are screened for inclusion in the survey if they are

willing and able to purchase the product. This is because the survey is meant

to represent that portion of the population (say, U.S. residents) who may be

willing to pay for the good or service. Respondents are anticipated to be

active in the purchase decision (or recently active) and are assumed to have

some knowledge of the brands and prices available in the marketplace.


36 See Allenby et al., supra note 6, at 638–40.

37 This survey format is known as a choice-based conjoint (CBC) survey.

Respondents are often instructed to assume that all other brand attributes

are constant across all alternatives. See id. at 641–42.


39 Id.


sells the exact same product (in terms of brand and other relevant

characteristics), but without this feature.40

In a number of cases in which conjoint analysis was used to value patent

damages, plaintiffs’ experts did not calculate the defendant’s MPP but instead

focused on calculating the price premium that a consumer would be willing to

pay for the infringing level of the attribute.41 This so-called consumer willingness

to pay (“consumer WTP”) was typically measured as the average part-worth of

the attribute level at issue, expressed in dollar terms.42 Plaintiffs’ experts then

estimated damages through a calculation that essentially multiplied average

consumer WTP by the defendant’s unit sales in the “infringing world.”43

Still, such an approach is inaccurate because, in fact, there is no

straightforward relationship between the calculation described above and the

defendant’s MPP.44 This is because the average consumer WTP for a particular

product feature does not dictate the market price of that product.45 The market

price of the defendant’s product in the “non-infringing world” is determined by

a variety of factors in addition to consumer preferences, including competition

40 Allenby et al., supra note 6, at 631–33.

41 See, e.g. Allenby et al., supra note 6, at 647. In our simple example, if a Wi-Fi

attribute is included in the camera, the camera infringes the patent. Thus, the

attribute itself infringes the patent. In other cases, however, there may be

multiple levels of the attribute, only one of which infringes the patent. For

example, one could imagine a case in which the Wi-Fi attribute could take

one of three levels—high speed, conventional speed, and none—and only

the high-speed level of the Wi-Fi attribute infringes the patent at issue.

42 See e.g. John R. Howell et al., Feature Valuation Using Equilibrium Analysis, in

HANDBOOK OF MARKETING ANALYTICS: METHODS AND APPLICATIONS IN

MARKETING MANAGEMENT, PUBLIC POLICY, AND LITIGATION SUPPORT *5

(Natalie Mizik & Dominique Hanssens eds., 2016) (unpublished manuscript)

(on file with author). Consumer WTP for a particular attribute level is

determined by dividing the part-worth of the attribute level (which is

measured in utils) by the part-worth of price in order to obtain a part-worth

expressed in dollar terms.


44 Some studies also consider the median consumer’s WTP. However, the same

issues with using consumer WTP instead of defendant’s MPP arise.

45 Allenby et al., supra note 6, at 652.


and cost considerations.46 Recent court decisions have also recognized that

damages calculations of this type are economically inappropriate.47

For example, in Visteon Glob. Tech., the plaintiff’s damages expert relied

primarily on a conjoint survey assessing consumer WTP for the infringing GPS

features at issue in the case.48 In assessing the credibility of plaintiff Visteon’s

damages expert and the reliability of his testimony, the court noted that his work

provided no evidence of how the defendant Garmin’s profit would have

increased at the time of the hypothetical negotiation from incorporating the

patented features.49 The court concluded that Visteon’s damages expert therefore

provided no evidence that would enable a jury to determine how much Garmin

would actually have been willing to pay to obtain the functionality of these

features.50 As a result of this and related considerations, the damages expert’s

testimony was ultimately excluded.51

Partially in response to critiques of the consumer WTP approach,

damages experts have focused on two other approaches for assessing the

defendant’s MPP: the Market Share Method (“MSM”) and the Equilibrium Profit

Method (“EPM”). The remainder of this paper explains each method and

concludes with a comparison of these two methods to the consumer WTP

approach.

A. Using the MSM to Assess the Defendant’s MPP

Under both the MSM and the EPM approaches, the damages expert

calculates the upper bound on damages as the difference between the

defendant’s profit in the “infringing world” and the “non-infringing world.”52

The key difference between the MSM and the EPM lies in how the defendant and

its competitors behave in the “non-infringing world.”

46 Howell et al., supra note 42, at *19. Two of the authors of the present paper

have published academic studies that specifically address this issue. See, e.g.,

Id.

47 See e.g., Visteon Glob. Tech., Inc. v. Garmin Int’l, Inc., No. 10-CV-10578, 2016

WL 5956325, at *6 (E.D. Mich. Oct. 14, 2016).

48 Id. at *2–7.

49 Id. at *17.

50 Id.

51 Id. at *19.

52 GLICK ET AL., supra note 7, at 144.


In order to simplify the calculation of the defendant’s “non-infringing

world” profit, the MSM assumes that the price of the defendant’s “non-

infringing world” product is the same as the price of its “infringing world”

product.53 The defendant’s profit in the “non-infringing world” is calculated as

its “non-infringing world” unit sales multiplied by its “non-infringing world”

operating margin (i.e., its “non-infringing world” price less its “non-infringing

world” costs).54 Because both elements of the “non-infringing world” operating

margin are assumed to be known, the only remaining element of the “non-

infringing world” profit calculation is the number of units sold.55 An example is

provided below that illustrates how the defendant’s “non-infringing world”

units can be calculated using the MSM.

In our example, we consider an “infringing world” in which there are

only two-competing cameras available: (i) the defendant’s (infringing) camera

and (ii) a single camera made by a non-infringing producer. 5 million customers

buy one of these two cameras; 2.5 million customers buy the infringing camera,

and 2.5 million buy the competitor’s camera. The defendant sells the infringing

camera at a price of $60, and its cost of producing this camera is $54, so the

“infringing world” operating margin is $6 per unit. Multiplying this $6 operating

margin by actual units sold (2.5 million), we obtain the defendant’s actual profit,

$15 million. 56

Next, we turn to the “non-infringing world” in which the defendant sells

a non-infringing (defeatured) version of its camera and the competitor’s camera

remains unchanged. Under the MSM, the price of the defendant’s defeatured

camera in the “non-infringing world” is assumed to be $60 (its “infringing

world” price). However, the defendant’s production cost decreases from $54 to

53 Id.

54 Id.

55 Id.

56 Here, we use the term “actual” to refer to figures observed in the real

world—as opposed to figures computed using the conjoint model. For the

sake of simplicity, this example abstracts from the fact that a damages expert

using the MSM will also typically use conjoint analysis to estimate

“infringing world” unit sales for reasons discussed further below.


$51 to reflect the infringing feature’s marginal cost of $3 per camera (assumed

known).57 Thus, the “non-infringing world” operating margin is $9 per unit.

In order to complete the calculation of the defendant’s “non-infringing

world” profit, we must calculate its “non-infringing world” unit sales.58 This

calculation relies on conjoint survey data to construct a model of consumer

demand for the products of interest.59 Let us assume that the plaintiff’s expert has

administered a conjoint survey to 400 respondents in order to determine their

valuations of various camera features. Conceptually, we can think about how

conjoint analysis is used in calculating the defendant’s “non-infringing world”

unit sales as a series of four steps.

First, the damages expert must determine how the 400 survey

respondents value the two cameras available in the infringing world.60 Table 2

presents—for a single survey respondent—sample valuations of these two

camera profiles based on the results of the conjoint analysis. Panel A provides

the respondent’s valuations for both the defendant’s camera and competitor’s

camera in the “infringing world”; Panel B provides the respondent’s valuation

for both cameras in the “non-infringing world.”61 Comparing column [2] and [4]

57 The defendant’s marginal cost of producing the infringing product and its

marginal cost of producing the infringing feature may be obtained through

the discovery process or estimated from the company’s public financial data.

Note that we assume that the defendant’s profit margin increases when it

produces a non-infringing version of the camera. This is a conservative

assumption from the plaintiff’s perspective, because it will make “non-

infringing world” profit larger, and therefore damages will be lower.


59 Id. at 638–45.

60 Id. at 642–43. Note that this is the world in which the defendant infringes the

patent. Competing producers, however, may not have similarly infringed, as

in this example.

61 For the sake of simplicity, this discussion abstracts away from the fact that,

for the statistical models implicitly underlying these estimates, there is

typically a random component to utility in addition to the “systematic”

component derived from part-worths. With this random component, we

only know that—for any individual consumer—the product with the higher

systematic valuation is more likely to be purchased than the product with

the lower systematic valuation. However, when we aggregate each

consumer’s decision over the entire market, we know the market share

associated with each product profile. To see this, consider a market with two


in Panel A, we see that the respondent values the defendant’s infringing camera

more than he values the sole competing camera; the respondent’s overall

valuation is forty utils for the defendant’s infringing camera62 and only twenty-

five utils for the competitor’s camera.63 Given that the respondent will purchase

the product for which he has the highest valuation, this particular respondent

would likely choose the defendant’s infringing camera over the competitor’s

camera.

Table 2. Hypothetical Respondent’s Valuations of Two Camera Profiles: Market

Share Method (MSM).

Infringing World Panel A

Defendant's Product Competitor's Product

Feature Part-worth Feature Part-worth

[1] [2] [3] [4]

Brand X 80 Z 65

Wi-Fi Yes 20 No 0

Resolution High 60 High 60

Price $60 -120 $50 -100

Total Valuation 40 25

goods (A and B) and a single type of consumer. Due to the random

component of utility, each consumer may have a 75% (25%) probability of

choosing product A (product B). This implies that, considering the market as

a whole, 75% of consumers pick product A and 25% pick product B. Allenby

et al. (2014) provide further detail on how model-based estimates of demand

are used to compute choice probabilities.

62 The higher the number of utils that an individual obtains from a product, the

more likely the individual will be to purchase that product.

63 Note that the (non-random) portion of each consumer’s valuation is

captured by the sum of his part-worths. Other consumers will have different

part-worths for a camera with this profile and therefore different overall

valuations.


Non-Infringing World Panel B



[1] [2] [3] [4]

Brand X 80 Z 65

Wi-Fi No 0 No 0


Price $60 -120 $50 -100


Second, the damages expert must determine survey respondents’

valuations of the defendant’s camera in the “non-infringing world” in which the

infringing feature has been removed.64 Returning to Table 2, Panel A column [2]

shows that in the “infringing world”, the hypothetical respondent values the

entire profile of the defendant’s camera at forty utils and the Wi-Fi element in

particular at twenty utils. Given this, we can predict that—in the “non-infringing

world” —the respondent will value the defendant’s defeatured camera at twenty

utils65 (see Panel B column [2]). Column [4] of Panel A and Panel B shows that the

respondent obtains twenty-five utils from buying the competing camera in both

the “infringing world” (see Panel A column [4]) and in the “non-infringing

world” (see Panel B column [4]). Thus, we predict that in the “non-infringing”

world, the respondent would be more likely to purchase the competing camera

(valued at twenty-five utils) than the defendant’s defeatured camera (valued at

twenty utils).

Third, the damages expert must compute market shares in the “non-

infringing world” by adding up the choices that each survey respondent made in

the prior step.66 (Recall that Table 1 represents just one survey respondent’s

preferences; other consumers will have different preferences.) To calculate

overall market shares, the damages expert must compare each respondent’s

valuations for three “non-infringing world” alternatives—the competing camera,

the defendant’s defeatured camera, and the no choice option.67 Recall that the


65 Given that the respondent values the entire profile of the defendant’s camera

at 40 forty utils and he values the infringing feature at 20 utils, we can

predict that he will value the defeatured camera at 40-20=20 utils.


67 Note that the estimation method typically allows each survey respondent to

have his own part-worths.


survey involves 400 respondents. Suppose that in the “non-infringing world,”

forty of the total respondents value the defendant’s defeatured camera more than

the competing camera or the no choice option. In that case, the survey expert can

conclude that, in the “non-infringing world,” ten percent of camera buyers will

choose the defendant’s defeatured camera. When we apply this ten percent

figure to the total population of camera buyers (assumed to be 5 million

consumers), we estimate the defendant’s unit sales in the “non-infringing world”

to be 0.5 million.

Fourth, the damages expert computes the defendant’s “non-infringing

world” profit.68 Under the MSM, this figure is calculated as the difference

between the actual price of the infringing camera ($60) and the actual cost of

producing the camera without the infringing feature ($51), multiplied by “non-

infringing world” units (0.5 million) determined in the previous step. This

calculation yields “non-infringing world” profit of $4.5 million ($9 x 0.5 million).

The last step in establishing the defendant’s MPP is determining the

defendant’s “infringing world” profit.69 In principle, one could calculate this

figure from accounting data on units actually sold by the defendant. As noted

above, with actual prices of $60, actual costs of $54, and actual units sold of 2.5

million, the defendant’s infringing world profit would be $15 million. The

difference between actual profit of $15 million and “non-infringing world” profit

of $4.5 million would provide a defendant’s MPP of $10.5 million.70


69 Id.

70 See supra note 61 (noting that the damages expert typically will not use

actual units sold in order to calculate “infringing world” profit. Noting

instead, that the expert will predict the number of infringing units based on

the results of the conjoint analysis, in the same way that he used conjoint

analysis to calculate “non-infringing world” units sold). The expert will

predict this way because—like all estimates—the “non-infringing world”

estimate of units sold always contains a degree of prediction error.

However, the expert can mitigate the impact of these prediction errors by

calculating the change in units sold as the difference between MSM

predicted units in the “infringing world” and MSM predicted units in the

“non-infringing world”; this differencing helps to cancel out the prediction

errors associated with each estimate. In contrast, if the expert compared

actual units sold (in the “infringing world”) to MSM-predicted unit sales (in

the “non-infringing world”), our damage results could be more heavily

influenced by these prediction errors.


B. Using the EPM to Assess the Defendant’s MPP

Although the MSM does tie the upper bound on damages to the

defendant’s MPP, the method is subject to criticism because it holds the

defendant’s “non-infringing world” price fixed. As a result, it does not allow the

defendant to adjust the price of its defeatured product in response to the actions

of its competitors or to any change in its production costs.

In contrast, the EPM provides a mechanism that allows the damages

expert to address these issues. Under this approach—just as under the MSM—

the damages expert calculates the defendant’s MPP as the difference between its

profit in the “infringing world” and the “non-infringing world.”71 Just as in the

case of the MSM, the focus is on the calculation of “non-infringing world” profit,

and we can again describe the analysis of the defendant’s “non-infringing world”

profit as a series of steps.

First, just as in the MSM, the damages expert must determine how the

conjoint survey respondents value the two cameras available in the infringing

world.72 Table 3 presents—for a hypothetical survey respondent—valuations of

the two camera profiles that we considered in our discussion of the MSM. Panel

A provides the “infringing world” attribute levels of the two cameras and their

associated part-worths, just as it did in Table 2.

Table 3. Hypothetical Respondent’s Valuations of Two Camera Profiles:

Equilibrium Profit Method (EPM).

Infringing World Panel A



[1] [2] [3] [4]

Brand X 80 Z 65

Wi-Fi Yes 20 No 0


Price $60 -120 $50 -100



72 See id. at 634–46.


Non-Infringing World Panel B



[1] [2] [3] [4]

Brand X 80 Z 65

Wi-Fi No 0 No 0


Price $56 -112 $51 -102


Second, unlike in our prior analysis, we allow both the defendant and its

competitor to re-optimize their prices once the infringing product is no longer

available on the market.73 In particular, the defendant may choose to reduce the

price of its defeatured product to: (i) offset the lower value that its defeatured

product provides to consumers and/or (ii) reflect the fact that the defendant’s

production costs for the defeatured product are lower than those for the

infringing product.74 At the same time, the competitor may choose to raise its

price to take advantage of its improved position vis-a-vis the defendant’s

product. Both the defendant and the competitor choose prices and quantities that

maximize their profit.75 Table 3, Panel B, Column [1] provides the features of the

defendant’s “non-infringing world” product, including its re-optimized price

(which has declined from $60 to $56), while Column [2] provides the associated

valuations. Likewise, Panel B, Column [3] provides the features of the

competitor’s “non-infringing world” product, which are unchanged relative to

those in the MSM approach except for the competitor’s re-optimized price

(which has increased from $50 to $51). Column [4] provides the associated

valuations.

73 Id. at 646.

74 Id. at 655–57.

75 The equilibrium concept that is commonly used in these cases is referred to

by economists as a Nash Bertrand equilibrium. Under this equilibrium

concept, each firm chooses its price such that it maximizes its profit given

the prices chosen by other firms. Because each firm has chosen a profit

maximizing price, none of the firms under study has a profit incentive to

change its market offering. Consistent with common practice, our discussion

of the EPM assumes that firms change prices rather than product features in

the “non-infringing” world.


Third, once optimal prices have been determined for each product in the

“non-infringing world,” the damages expert can then compute “non-infringing

world” unit sales.76 As in the MSM, the damages expert calculates each survey

respondent’s valuation for the various alternatives, given the optimal price for

the defeatured camera that was calculated in the prior step. Each respondent is

assumed to purchase the camera that provides him with the greatest value (or

forego purchase if the “no choice” option provides the greatest utility).

Fourth, the damages expert computes the defendant’s “non-infringing

world” sales by adding up the choices made by each survey respondent in the

prior step.77 Recall that our hypothetical conjoint survey involved 400

respondents. Suppose that the defendant lowers the price of its defeatured

camera so that 140 respondents assign the highest valuation to the defendant’s

defeatured camera. In that case, the survey expert can conclude that—in the

“non-infringing world”—35% will choose the defendant’s defeatured camera.78

Recall that the entire population of camera buyers is 5 million. Thus, in the “non-

infringing world”, the defendant will sell 1.75 million (defeatured) cameras.

Finally, the damages expert computes the defendant’s MPP as the

difference between the defendant’s “infringing world” and “non-infringing

world” profit.79 With an operating margin of $5 and sales of 1.75 million units,

the defendant’s “non-infringing world” profit is $8.75 million. As in the case of

the MSM, the defendant’s “infringing world” profit under the EPM could—in

principle—be calculated using real world accounting data on prices and units

sold. If that were done in this case, the defendant’s “infringing world” profit

would be $15 million and the defendant’s MPP would be the difference between

$15 million and $8.75 million, or $6.25 million.80


77 Id. at 657.

78 Recall that the number of consumers who would still buy the defendant’s

product was only 0.5 million under the MSM. The increase in the

defendant’s market share in the EPM results from the price re-optimization

described in the second step of Section IV.B.


80 In practice, however, the defendant’s “infringing world” price and unit

sales, like its “non-infringing world” price and unit sales, are predicted

using the EPM, for the same reasons that “infringing world” unit sales are

predicted using the conjoint model under the MSM. See supra note 70.


V. CONCLUSIONS: COMPARISON OF APPROACHES USING CONJOINT

ANALYSIS TO ASSESS DAMAGES

In a number of high stakes patent infringement cases, experts have

introduced evidence based on conjoint analysis to calculate reasonable royalty

damages.81 These analyses have been approached in a variety of ways. Although

some damages experts have used what we refer to as the consumer WTP

approach, this approach has been justly criticized.82 This is because there is no

straightforward relationship between the outcome of this approach and

defendant’s MPP, which is the difference between the defendant’s profit in the

“infringing world” and the “non-infringing world.”83

Two other methodologies, the MSM and the EPM, avoid this problem.

Under both of these methods, the damages expert calculates the defendant’s

MPP when it provides an upper bound on damages. The key difference between

the MSM and the EPM is in their treatment of how the defendant and its

competitors behave in the “non-infringing world.”84

The MSM is the simpler approach and requires less data for its

implementation.85 Nonetheless, its simplifying assumption—that the defendant

charges the same price for its “infringing world” product and its “non-infringing

world” product—is subject to criticism.86 As a result of this assumption, the MSM

approach will overstate the defendant’s MPP, and thus overstate the plaintiff’s

damages.87

While we would expect the defendant’s “non-infringing world” sales

(and profit) to decline relative to “infringing world” sales (and profit), the

defendant could mitigate this decline by lowering its price in the “non-infringing

world.” Because the MSM assumes that the defendant charges the same price in

81 See, e.g., supra note 1.

82 See supra Part IV.

83 Id.

84 Id.

85 See supra Section IV.A.

86 Id.

87 Id. In our numerical examples, we showed that—under the MSM—the

defendant’s MPP was almost 70% greater than that produced by the EPM.

Under the MSM, the defendant’s MPP was $10.5 million, while under the

EPM, the defendant’s MPP was $6.25 million.


the “infringing world” and in the “non-infringing world,” the MSM will produce

“non-infringing world” profit that is—from an economic perspective—too low,

making MSM-based damages too high.88

In contrast, the EPM provides a more theoretically sound damages

estimate, because it takes into account the competitive interactions of the

defendant and its rivals and provides a more unified framework for addressing

changes in production costs. The EPM, however, involves more complex

calculations. It also requires the damages expert to make assumptions about the

nature of strategic interactions among competitors and inferences about

competitors’ costs, all of which may be vulnerable to criticism depending on how

closely they reflect reality.89 Thus, those deciding between the EPM and the MSM

must carefully consider these costs and benefits in selecting their damages

methodology.

88 Id.

89 See discussion supra Section IV.B.

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